True or False? All digits of an integer number are significant if the last digit is non-zero.

True. All digits of an integer number are significant if the last digit is non-zero. For example, 702 has 3 significant figures

True or False? Zeros at the end of an integer number are always significant.

False. Zeros at the end of an integer number are never significant. For example, 306 000 has 3 significant figures

True or False? Zeros in front of an integer number are never significant.

True. Zeros in front of an integer number are never significant. For example, 0.025 has 2 significant figures

True or False? Zeros at the end of a number less than one are never significant.

False. Zeros at the end of a number less than one are always significant. For example, 0.02000 has 4 significant figures

True or False? Zeros after an integer number that has a decimal point are always significant.

True. Zeros after an integer number that has a decimal point are always significant. For example, 40.0 has 3 significant figures

Define a scalar quantity.

A scalar quantity is a quantity that has magnitude but not direction.

What is a vector quantity?

A vector quantity is a quantity that has both magnitude and direction .

True or False? Mass is a scalar quantity.

True. Mass is a scalar quantity as it has only magnitude.

True or False? Distance is a vector quantity.

False. Distance is a scalar quantity.

Is 300 N a scalar or vector quantity?

300 N is a vector quantity. Newtons (N) are the unit of force , and force has both magnitude and direction ; therefore, force is a vector quantity.

Is 100 km due north a scalar or a vector quantity?

100 km due north is a vector quantity because it includes both a magnitude and a direction .

True or False? Energy is a scalar quantity.

True Energy is a scalar quantity. It has magnitude, but not direction.

Is temperature a scalar or a vector?

Temperature is a scalar quantity.

True or False? Weight is a scalar quantity.

False. Weight is a force, so it is a vector quantity. Mass is a scalar quantity.

What is the difference between speed and velocity?

Speed is a scalar quantity with only magnitude. Velocity is a vector quantity with both magnitude and direction.

State another name for the net vector .

Another name for the resultant vector is a resultant vector.

State the names of the two geometric methods used to combine vectors using addition or subtraction.

The names of the two methods used to combine vectors are: triangle method parallelogram method

True or False? The product of a scalar, mass, and a vector, acceleration, is a scalar.

False. The product of a scalar, mass, and a vector, acceleration, is a vector , force.

What is the opposite of combining vectors?

The opposite of combining vectors is resolving vectors.

True or False? A single resultant vector can be resolved into two vectors with the same effect as the original one.

True. A single resultant vector can be resolved into two vectors with the same effect as the original one.

How is the direction of a resultant vector measured?

The direction of a resultant vector is measured as the angle with respect to the vertical or the horizontal .

State the mathematical technique used to calculate the angle of a resultant vector.

The mathematical technique used to calculate the angle of a resultant vector is trignonometry .

State a non-algebraic method that can be used to combine or resolve vectors.

The non-algebraic method that can be used to combine or resolve vectors is scale drawing .

State the equipment needed to draw the lengths and angles of vectors accurately using a scale drawing.

The equipment needed to draw the lengths and angles of vectors accurately using a scale drawing is: pencil ruler protractor

What is a derived unit ?

A derived unit is one that is made up of combinations of SI units.

What is the SI base unit for mass ?

The SI base unit for mass is kilograms (kg).

True or False? The SI base unit for the newton is kg m s –1 .

False. The SI base unit for the newton is kg m s –2

What is the SI base unit for length ?

The SI base unit for length is metres (m).

True or False? The SI base unit for the joule is kg m s –2 .

False. The SI base unit for the joule is kg m 2 s –2 .

What is the SI base unit for time ?

The SI base unit for time is seconds (s).

True or False? The SI base unit for the watt is kg m 2 s –3 .

True. The SI base unit for the watt is kg m 2 s –3 .

What is the SI base unit for current ?

The SI base unit for current is amperes , or amps (A).

True or False? The SI base unit for the pascal is kg m –1 s –2 .

True. The SI base unit for the pascal is kg m –1 s –2

What is the SI base unit for temperature ?

The SI base unit for temperature is the kelvin (K).

True or False? The SI base unit for frequency is hertz (Hz).

False. The unit for frequency is hertz (Hz), but the SI base unit is s –1 .

What is the SI base unit for the amount of a substance?

The SI base unit for the amount of a substance is the mole (mol).

What is dimensional analysis ?

Dimensional analysis is a method used to check the homogeneity of physical equations by studying the units.

If a length is measured as 15.3 ± 0.2 cm, what is the absolute uncertainty in the measurement?

The absolute uncertainty in the measurement is ± 0.2 cm . length = 15.3 ± 0.2 cm measurement = 15.3 cm absolute uncertainty = ± 0.2 cm

How do you find the uncertainty in a reading ?

The uncertainty in a reading is ± half the smallest division.

How do you find the uncertainty in a measurement ?

The uncertainty in a measurement is at least ±1 smallest division.

How do you find the uncertainty of a set of readings ?

The uncertainty in a set of readings is half the range, or ± ½ (largest - smallest value).

True or False? When adding or subtracting data, the combined uncertainty is the sum of their percentage uncertainties.

False. When adding or subtracting data, the combined uncertainty is the sum of their absolute uncertainties.

True or False? When multiplying or dividing data, the combined uncertainty is the sum of their fractional or percentage uncertainties.

True. When multiplying or dividing data, the combined uncertainty is the sum of their fractional or percentage uncertainties.

What is the rule for propagating the uncertainty of a quantity which is raised to a power?

When a quantity is raised to a power, multiply the fractional or percentage uncertainty by the power.

If two measured lengths, 12.3 ± 0.2 cm and 7.8 ± 0.1 cm, are added together, what is their combined uncertainty?

Combined uncertainty = 0.2 cm + 0.1 cm = 0.3 cm When adding data, the combined uncertainty is the sum of their absolute uncertainties.

Find the percentage uncertainty in speed when dividing a distance measurement 4.5 m ± 2% by a time measurement 1.2 s ± 1%.

Percentage uncertainty in speed = 2% + 1% = 3% . When dividing data, the combined uncertainty is the sum of the percentage uncertainties.

What do error bars show on a graph?

Error bars are lines drawn above and below (or from side to side of) a point on a graph to show the absolute uncertainty of that measurement.

True or False? Error bars on a graph must all be the same size.

False. Error bars on a graph can have different sizes as they represent different uncertainties for each data point.

Define a line of best fit .

A line of best fit is a line that passes as close to all plotted points as possible on a graph.

What is the difference between a 'best' and 'worst' line of best fit?

A 'best' line of best fit is a line that passes as close to all plotted points as possible on a graph. A 'worst' line of best fit is either the steepest or shallowest possible line that fits within all the error bars on a graph.

What is percentage difference?

Percentage difference is an indication of how close the experimental value is to the accepted value.

IBPhysicsDPHLFlashcardsToolsTool 3: Mathematics

Tool 3: Mathematics (DP IB Physics) Flashcards

1/79

0Still learning

Know0

FrontApplying General Mathematics in Physics
What is the order of magnitude of $6.32 \times 10^{8}$ ?

Did this page help you?

Cards in this collection (79)

What is the order of magnitude of $6.32 \times 10^{8}$ ?
The order of magnitude of $6.32 \times 10^{8}$ is: $10^{9}$
What is the order of magnitude of $1.60 \times 10^{- 19}$ ?
The order of magnitude of $1.60 \times 10^{- 19}$ is: $10^{- 19}$
What is the order of magnitude of $7.81 \times 10^{- 9}$ ?
The order of magnitude of $7.81 \times 10^{- 9}$ is: $10^{- 8}$
True or False?
1000 is one order of magnitude larger than 100.
True.
One order of magnitude larger is ten times larger.
- $10 \times 100 = 1000$
True or False?
$10^{28}$ is two orders of magnitude larger than $5.6 \times 10^{26}$ .
False.
Two orders of magnitude larger than $5.6 \times 10^{26}$ is $10^{29}$ .
The order of magnitude of $5.6 \times 10^{26}$ is $10^{27}$ .
Two orders of magnitude larger is one hundred times larger.
- $10^{27} \times 10^{2} = 10^{29}$
Estimate the order of magnitude of the diameter of a hydrogen atom.
The order of magnitude of the diameter of a hydrogen atom is $~ 10^{- 10}$ m.
Estimate the order of magnitude of the length of a car.
The order of magnitude of the length of a car is $~ 10^{0}$ m.
Estimate the order of magnitude of the diameter of the Earth.
The order of magnitude of the diameter of the Earth is $~ 10^{7}$ m.
What is $426 019$ in scientific notation to one significant figure?
$426 019$ in scientific notation to one significant figure is $4 \times 10^{5}$ .
What is $105 026 132$ in scientific notation to two significant figures?
$105 026 132$ in scientific notation to two significant figures is $1.1 \times 10^{8}$ .
What is $0.002053$ in scientific notation to two significant figures?
$0.002053$ in scientific notation to two significant figures is $2.1 \times 10^{- 3}$ .
True or False?
All digits of an integer number are significant if the last digit is non-zero.
True.
All digits of an integer number are significant if the last digit is non-zero.
- For example, 702 has 3 significant figures
True or False?
Zeros at the end of an integer number are always significant.
False.
Zeros at the end of an integer number are never significant.
- For example, 306 000 has 3 significant figures
True or False?
Zeros in front of an integer number are never significant.
True.
Zeros in front of an integer number are never significant.
- For example, 0.025 has 2 significant figures
True or False?
Zeros at the end of a number less than one are never significant.
False.
Zeros at the end of a number less than one are always significant.
- For example, 0.02000 has 4 significant figures
True or False?
Zeros after an integer number that has a decimal point are always significant.
True.
Zeros after an integer number that has a decimal point are always significant.
- For example, 40.0 has 3 significant figures
Define a scalar quantity.
A scalar quantity is a quantity that has magnitude but not direction.
What is a vector quantity?
A vector quantity is a quantity that has both magnitude and direction.
True or False?
Mass is a scalar quantity.
True.
Mass is a scalar quantity as it has only magnitude.
True or False?
Distance is a vector quantity.
False.
Distance is a scalar quantity.
Is 300 N a scalar or vector quantity?
300 N is a vector quantity. Newtons (N) are the unit of force, and force has both magnitude and direction; therefore, force is a vector quantity.
Is 100 km due north a scalar or a vector quantity?
100 km due north is a vector quantity because it includes both a magnitude and a direction.
True or False?
Energy is a scalar quantity.
True
Energy is a scalar quantity. It has magnitude, but not direction.
Is temperature a scalar or a vector?
Temperature is a scalar quantity.
True or False?
Weight is a scalar quantity.
False.
Weight is a force, so it is a vector quantity. Mass is a scalar quantity.
What is the difference between speed and velocity?
Speed is a scalar quantity with only magnitude. Velocity is a vector quantity with both magnitude and direction.
State the possible ways vectors can be combined or resolved.
The possible ways vectors can be changed are:
- Combining through vector addition or subtraction
- Combining through vector multiplication
- Resolving into components through trigonometry
State another name for the net vector.
Another name for the resultant vector is a resultant vector.
State the names of the two geometric methods used to combine vectors using addition or subtraction.
The names of the two methods used to combine vectors are:
- triangle method
- parallelogram method
True or False?
The product of a scalar, mass, and a vector, acceleration, is a scalar.
False.
The product of a scalar, mass, and a vector, acceleration, is a vector, force.
What is the opposite of combining vectors?
The opposite of combining vectors is resolving vectors.
True or False?
A single resultant vector can be resolved into two vectors with the same effect as the original one.
True.
A single resultant vector can be resolved into two vectors with the same effect as the original one.
How is the direction of a resultant vector measured?
The direction of a resultant vector is measured as the angle with respect to the vertical or the horizontal.
State the mathematical technique used to calculate the angle of a resultant vector.
The mathematical technique used to calculate the angle of a resultant vector is trignonometry.
State the equation for the vertical component of the force $F$ at an angle $θ$ to the horizontal shown in the diagram.
The equation for the vertical component of the force $F$ at an angle $θ$ to the horizontal shown in the diagram is $F_{y} = F \sin θ$
Where:
- $F$ = resultant force, measured in newtons (N)
- $θ$ = angle of resultant force to horizontal, measured in degrees ( $°$ )
State the equation for the horizontal component of the force $F$ at an angle $θ$ to the horizontal shown in the diagram.
The equation for the horizontal component of the force $F$ at an angle $θ$ to the horizontal shown in the diagram is $F_{x} = F \cos θ$
Where:
- $F$ = resultant force, measured in newton's (N)
- $θ$ = angle of resultant force to horizontal, measured in degrees ( $°$ )
State a non-algebraic method that can be used to combine or resolve vectors.
The non-algebraic method that can be used to combine or resolve vectors is scale drawing.
State the equipment needed to draw the lengths and angles of vectors accurately using a scale drawing.
The equipment needed to draw the lengths and angles of vectors accurately using a scale drawing is:
- pencil
- ruler
- protractor
A scale of 2 cm = 1 km is given in a vector scale diagram. State the actual distance represented by 5 cm in the scale diagram.
The actual distance represented by 5 cm in the scale diagram is 2.5 km.
- $\frac{2 cm}{2} \times 5 = \frac{1 km}{2} \times 5$
- $5 cm = \frac{5}{2} km$
State the length of the 5.0 kN force on the scale drawing.
The length of the 5.0 kN force on the scale drawing is 5 cm.
A scale of 5 cm = 15 km is given in a vector scale diagram. State the actual distance represented by 7.5 cm in the scale diagram.
The actual distance represented by 7.5 cm in the scale diagram is 22.5 km.
- $\frac{5 cm}{5} \times 7.5 = \frac{15 km}{5} \times 7.5$
- $7.5 cm = \frac{45}{2} km$
What is a derived unit?
A derived unit is one that is made up of combinations of SI units.
What is the SI base unit for mass?
The SI base unit for mass is kilograms (kg).
True or False?
The SI base unit for the newton is kg m s^–1.
False.
The SI base unit for the newton is kg m s^–2
What is the SI base unit for length?
The SI base unit for length is metres (m).
True or False?
The SI base unit for the joule is kg m s^–2.
False.
The SI base unit for the joule is kg m² s^–2.
What is the SI base unit for time?
The SI base unit for time is seconds (s).
True or False?
The SI base unit for the watt is kg m² s^–3.
True.
The SI base unit for the watt is kg m² s^–3.
What is the SI base unit for current?
The SI base unit for current is amperes, or amps (A).
True or False?
The SI base unit for the pascal is kg m^–1 s^–2.
True.
The SI base unit for the pascal is kg m^–1 s^–2
What is the SI base unit for temperature?
The SI base unit for temperature is the kelvin (K).
True or False?
The SI base unit for frequency is hertz (Hz).
False.
The unit for frequency is hertz (Hz), but the SI base unit is s^–1.
What is the SI base unit for the amount of a substance?
The SI base unit for the amount of a substance is the mole (mol).
What is dimensional analysis?
Dimensional analysis is a method used to check the homogeneity of physical equations by studying the units.
Show that the equation $p = m v$ is a homogeneous equation.
An equation is homogeneous if the SI base units are the same on both sides.
- $p = m v$
- $[kg m s^{- 1}] = [kg] \times [m s^{- 1}]$
- $[kg m s^{- 1}] = [kg m s^{- 1}]$
Show that the equation $E_{k} = \frac{p^{2}}{2 m}$ is a homogeneous equation.
An equation is homogeneous if the SI base units are the same on both sides.
- $E_{k} = \frac{p^{2}}{2 m}$
- $[kg m^{2} s^{- 2}] = \frac{[{kg}^{2} m^{2} s^{- 2}]}{[kg]}$
- $[kg m^{2} s^{- 2}] = [kg m^{2} s^{- 2}]$
Show that the equation $P = F v$ is a homogeneous equation.
An equation is homogeneous if the SI base units are the same on both sides.
- $P = F v$
- $\frac{[kg m^{2} s^{- 2}]}{[s]} = [kg m s^{- 2}] \times [m s^{- 1}]$
- $[kg m^{2} s^{- 3}] = [kg m^{2} s^{- 3}]$
Show that the equation $T = 2 π \sqrt{\frac{m}{k}}$ is a homogeneous equation.
An equation is homogeneous if the SI base units are the same on both sides.
- $T = 2 π \sqrt{\frac{m}{k}}$
- $\frac{1}{[s]} = \sqrt{\frac{[kg]}{[N m^{- 1}]}} = \sqrt{\frac{[kg]}{[kg m s^{- 2}] [m^{- 1}]}}$
- $\frac{1}{[s]} = \sqrt{\frac{1}{[s^{- 2}]}} = \frac{1}{[s]}$
If a length is measured as 15.3 ± 0.2 cm, what is the absolute uncertainty in the measurement?
The absolute uncertainty in the measurement is ± 0.2 cm.
- length = 15.3 ± 0.2 cm
- measurement = 15.3 cm
- absolute uncertainty = ± 0.2 cm
If a current is measured as 5.5 ± 0.1 A, what is the fractional uncertainty in the measurement?
The fractional uncertainty in the measurement is ± 0.02.
- current = 5.5 ± 0.1 A
- measurement = 5.5 A
- fractional uncertainty = $\frac{0.1}{5.5}$ = ± 0.02
If a mass is measured as 250 ± 5 g, what is the percentage uncertainty in the measurement?
The percentage uncertainty in the measurement is ± 2%.
- mass = 250 ± 5 g
- measurement = 250 g
- percentage uncertainty = $\frac{5}{250} \times 100 %$ = ± 2%
How do you find the uncertainty in a reading?
The uncertainty in a reading is ± half the smallest division.
How do you find the uncertainty in a measurement?
The uncertainty in a measurement is at least ±1 smallest division.
How do you find the uncertainty of a set of readings?
The uncertainty in a set of readings is half the range, or ± ½ (largest - smallest value).
True or False?
When adding or subtracting data, the combined uncertainty is the sum of their percentage uncertainties.
False.
When adding or subtracting data, the combined uncertainty is the sum of their absolute uncertainties.
True or False?
When multiplying or dividing data, the combined uncertainty is the sum of their fractional or percentage uncertainties.
True.
When multiplying or dividing data, the combined uncertainty is the sum of their fractional or percentage uncertainties.
What is the rule for propagating the uncertainty of a quantity which is raised to a power?
When a quantity is raised to a power, multiply the fractional or percentage uncertainty by the power.
If two measured lengths, 12.3 ± 0.2 cm and 7.8 ± 0.1 cm, are added together, what is their combined uncertainty?
Combined uncertainty = 0.2 cm + 0.1 cm = 0.3 cm
When adding data, the combined uncertainty is the sum of their absolute uncertainties.
Find the percentage uncertainty in speed when dividing a distance measurement 4.5 m ± 2% by a time measurement 1.2 s ± 1%.
Percentage uncertainty in speed = 2% + 1% = 3%.
When dividing data, the combined uncertainty is the sum of the percentage uncertainties.
A cylinder of volume $V = π r^{2} h$ has a radius of 5.0 ± 0.2 cm and a height of 10.0 ± 0.5 cm. Calculate the percentage uncertainty in the volume.
Percentage uncertainty in volume = 13%.
- $(\frac{∆ V}{V}) = 2 (\frac{∆ r}{r}) + (\frac{∆ h}{h})$
- $(\frac{∆ V}{V}) = 2 (\frac{0.2}{5.0}) + (\frac{0.5}{10.0}) = 0.13$
- percentage uncertainty = $0.13 \times 100 % = 13 %$
What do error bars show on a graph?
Error bars are lines drawn above and below (or from side to side of) a point on a graph to show the absolute uncertainty of that measurement.
True or False?
Error bars on a graph must all be the same size.
False.
Error bars on a graph can have different sizes as they represent different uncertainties for each data point.
Define a line of best fit.
A line of best fit is a line that passes as close to all plotted points as possible on a graph.
What is the difference between a 'best' and 'worst' line of best fit?
A 'best' line of best fit is a line that passes as close to all plotted points as possible on a graph.
A 'worst' line of best fit is either the steepest or shallowest possible line that fits within all the error bars on a graph.
State the equation for percentage uncertainty in gradient.
The equation for percentage uncertainty in gradient is:
- percentage uncertainty = $\frac{b e s t g r a d i e n t - w o r s t g r a d i e n t}{b e s t g r a d i e n t} \times 100 %$
What is percentage difference?
Percentage difference is an indication of how close the experimental value is to the accepted value.
State the equation for percentage difference.
The equation for percentage difference is:
- percentage difference = $\frac{e x p e r i m e n t a l v a l u e - a c c e p t e d v a l u e}{a c c e p t e d v a l u e} \times 100 %$
True or False?
The smaller the percentage difference, the greater the accuracy of the results of the experiment.
True.
The smaller the percentage difference, the greater the accuracy of the results of the experiment.
Draw the lines of maximum and minimum gradient on the graph.
The lines of maximum and minimum gradient on the graph are:

Previous:Scalars & VectorsNext:Inquiry 1: Exploring and Designing in Physics

Tool 3: Mathematics (DP IB Physics) Flashcards

Cards in this collection (79)

Space, Time & Motion

Kinematics

Forces & Momentum

Work, Energy & Power

Rigid Body Mechanics

Galilean & Special Relativity

The Particulate Nature of Matter

Thermal Energy Transfers

Greenhouse Effect

Gas Laws

Thermodynamics

Current & Circuits

Wave Behaviour

Simple Harmonic Motion

Wave Model

Wave Phenomena

Standing Waves & Resonance

Doppler Effect

Fields

Gravitational Fields

Electric & Magnetic Fields

Motion in Electromagnetic Fields

Induction

Nuclear & Quantum Physics

Structure of the Atom

Quantum Physics

Radioactive Decay

Fission

Fusion & Stars

Tools

Measurements in Physics

Processing Uncertainties

Scalars & Vectors

Tool 3: Mathematics

Inquiry Process

Inquiry 1: Exploring and Designing in Physics

Inquiry 2: Collecting and Processing Data in Physics

Inquiry 3: Concluding and Evaluating in Physics